If you didn't have an MX record you would probably not be receiving some mail.
Have you checked to see if your ip is on any rbls ? Have you looked at the header of the email that arrives at gmail/hotmail ? Hard to really help you with the domain.
As pointed out... you probably dont receive mail for this domain if you have no MX records.
for my particular zone.. here's the entries in my zone file for my MX records and SPF record.
IN MX 1 ASPMX.L.GOOGLE.COM.
IN MX 5 ALT1.ASPMX.L.GOOGLE.COM.
IN MX 5 ALT2.ASPMX.L.GOOGLE.COM.
IN MX 10 ASPMX2.GOOGLEMAIL.COM.
IN MX 10 ASPMX3.GOOGLEMAIL.COM.
IN MX 10 ASPMX4.GOOGLEMAIL.COM.
IN MX 10 ASPMX5.GOOGLEMAIL.COM.
IN TXT "v=spf1 a mx ~all"
As you can see, I use Google Apps/ie GMail for Domains for my domain...
the SPF record also states that mail can come from any hosts matching the MX records, and that combined list should contain all the hosts that would deliver mail for the domain and anything else sending mail from my domain should result in a softfail on an SPF check.
The lowest number in the MX record (1,5,10s in the examles above) has the highest precedence.
I didn't think HotMail did email services for 3rd party domains.
Well, it's done under the Windows Live services stuff...
So, your asking about setting up HotMail as the MX records for your domain seems, uh, wrong somewhere...Why
Why would anyone use HotMail anyways? :p
(Ok, I'm still bitter about going to an interview for HotMail being told to dress casual then getting chewed out for dressing casual and not wearing a suit. With them telling me Bill Gates would never do that.)